Quotation Frühwirth-Schnatter, Sylvia. 2004. Gibbs Sampling for Time Series of Small Counts. COMPSTAT 2004, Prag, Tschechische Republik, 23.08.-27.08.




In this paper we consider time series of counts where the observed process yt is assumed to follow a Poisson distribution: yt ∼ Poisson (λt) and the effect of exogenous variables zt, for independent observations is captured through a log-linear model where λt = exp(z′tβ). To account for the dependency likely to be present in time series data of counts, various extensions of the log-linear model have been suggested which, following Cox (1981), may be classified into parameter-driven and observation-driven models. While observations-driven models are easy to estimate, their theoretical properties can be difficult to derive in comparison to parameter-driven models. Here we deal with parameter-driven models, where the conditional distribution of yt is allowed to change over time and this change is driven by a latent process. Estimation of parameter-driven Poisson time series models is known to be a challenging problem. Maximum likelihood estimation of these models is hampered by the fact that the marginal likelihood, where the latent process is integrated out, is in general not available in closed form. Alternatively, estimation of these models is also feasible within a Bayesian framework using data augmentation and Markov chain Monte Carlo (MCMC) methods. A major difficulties with any of the existing MCMC approaches is that practical implementation requires the use of aMetropolis-Hastings algorithm for at least for part of the unknown parameter vector, which in turns make it necessary to define suitable proposal densities in rather high-dimensional parameter spaces. Single-move sampling for this type of models is known to be potentially very inefficient, see e.g. [1].


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Paper presented at an academic conference or symposium
Language English
Title Gibbs Sampling for Time Series of Small Counts
Event COMPSTAT 2004
Year 2004
Date 23.08.-27.08
Country Czech Republic
Location Prag
URL http://compstat2004.cuni.cz/


Frühwirth-Schnatter, Sylvia (Details)
Institute for Statistics and Mathematics IN (Details)
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